Hydrodynamic Force and Rise Velocity of an Interactive Bubble due to a Laminar Wake Effect

Abstract

The interaction between two spherical bubbles rising in-line in a stagnant Newtonian liquid was studied. A model was proposed to relate the flow structure in the wake of a leading bubble with the hydrodynamic force and the rise velocity of a trailing bubble, at separation distances of the order of its diameter (2 ? s/d _B  ? 14) and moderate particle Reynolds numbers (20 ? Re ₁ ? 200). To this end, a force balance on the trailing bubble was used as a starting point. The flow character in the axisymmetric laminar wake of a spherical bubble was analyzed, and an equation for the axial velocity profile was proposed in the modified form of an analytical approximation, which was fitted to numerical data. This equation, once substituted in the force balance, allowed obtaining a predictive model explaining quantitatively the in-line interaction of a pair of bubbles in terms of the average axial velocity in the leading bubble wake. The predictions of the proposed models show a good agreement with numerical and experimental data for the hydrodynamic force and the rise velocity of a trailing bubble, respectively.